Feigenbaum diagram of the logistic equation

The logistic equation is defined as:

xn+1=r xn(1-xn)

The logistic equation is a mathematical model for the growth of a population depending on a parameter r. r may for example be the amount of food available to a given species while x means the number of members of this species in a given ecosystem.

The Feigenbaum diagram shows values for x on the vertical axis as they are calculated for different values of the parameter r (horizontal axis). You may change r and click the 'redraw' button. Values of r greater than 4.0 are forbidden. The first 400 x-values for each parameter value are not shown, the next 300 values are plotted.

A Java applet appears here.

Peter Uelkes
Last modified: Sat Dec 30 16:39:17 CET 2000